The estimated cost to rebuild a popular running and bike trail along a proposed light-rail Purple Line between Bethesda and Silver Spring has almost doubled, to about $95 million, Montgomery County officials said Thursday.

The projected $45 million increase comes after Montgomery County officials have promised for years that a trail would remain, even after trains began running through what many now consider to be a wooded oasis in the heavily developed Maryland suburbs.

The expense of building the four-mile trail, previously budgeted to cost $49.5 million, would be the county’s responsibility. The Maryland Transit Administration (MTA) would be responsible for most of the 16-mile rail line’s construction costs, now projected at $2.37 billion.

Gary Erenrich, a special assistant to the director of Montgomery County’s Transportation Department, said County Executive Isiah Leggett (D) will update his six-year capital budget proposal to reflect the higher figures.

Montgomery County Council member Roger Berliner (D-Potomac-Bethesda), whose district includes the trail, said its reconstruction remains “inseparable” from the Purple Line project.

“People have appreciated for some time that we have a deal here,” Berliner said.

But Jim Roy, a board member for Friends of the Capital Crescent Trail, which opposes the trail alignment, recalled that state and county officials previously said the trail and Purple Line would remain in a tunnel beneath busy Wisconsin Avenue in downtown Bethesda. When the tunnel plan’s cost estimate jumped, officials diverted the trail onto local streets.

“The MTA and pro-Purple Line people have made numerous promises about what we could expect,” Roy said, “and a lot of those promises are being broken.”

Berliner and Erenrich said county officials considered the previous trail estimate to be a budget placeholder that would grow as engineering progressed. The MTA has now designed about 30 percent of the project.

Some of the higher costs stemmed from county requests to widen the trail from 10 to 12 feet to provide better emergency vehicle access and add lighting, officials said.

“We wanted to make this a really good trail,” Berliner said.

Montgomery County bought the trail land from a freight railroad in 1988 to preserve it for a transitway and interim trail.

The interim trail, known as the Georgetown Branch of the Capital Crescent Trail, now ends on the east in Lyttonsville, where cyclists and runners must use local streets to reach downtown Silver Spring. Plans for a regional trail network call for the Capital Crescent Trail to be extended into Silver Spring, where it would connect to the District’s Metropolitan Branch Trail after its northern segment is completed.

“The goal is you could bike from Georgetown to Bethesda to Silver Spring and into Union Station on one continuous trail,” said Greg Billing, advocacy coordinator for the Washington Area Bicyclist Association. “All that hinges on finishing the gap between Bethesda and Silver Spring.”

Wayne Phyillaier, a Purple Line advocate and past chairman of the Coalition for the Capital Crescent Trail, said he believes political pressure from trail users would prevent local officials from backing off the trail plan.

“You can imagine the outcry if they walked away from this,” he said.

Erenrich said county and state officials are discussing whether the state will help cover some of the costs, such as for retaining walls that would separate the trail and train tracks.

State officials have said they hope to begin construction on a Purple Line in 2015 and begin operating it in 2020.